There is a great need in the semiconductor industry for metrology equipment that can provide high resolution, nondestructive evaluation of product wafers as they pass through various fabrication stages. In recent years, a number of products have been developed for the nondestructive evaluation of semiconductor samples. One such product has been successfully marketed by the assignee herein under the trademark Therma-Probe (TP). This device incorporates technology described in the following U.S. Pat. Nos. 4,634,290; 4,646,088; 5,854,710; 5,074,669 and 5,978,074. Each of these patents is incorporated herein by reference.
In the basic device described in the patents, an intensity modulated pump laser beam is focused on the sample surface for periodically exciting the sample. In the case of a semiconductor, thermal and plasma waves are generated in the sample that spread out from the pump beam spot. These waves reflect and scatter off various features and interact with various regions within the sample in a way that alters the flow of heat and/or plasma from the pump beam spot.
The presence of the thermal and plasma waves has a direct effect on the reflectivity at the surface of the sample. As a result, subsurface features such as damage produced by ion implantation, defects and non-uniformity of carrier concentration, alter the passage of the thermal and plasma waves and have a direct effect on the optical reflective patterns at the surface of the sample. By monitoring the changes in reflectivity of the sample at the surface, information about characteristics below the surface can be investigated.
In the basic device, a second laser is provided for generating a probe beam of radiation. This probe beam is focused collinearly with the pump beam and reflects off the sample. A photodetector is provided for monitoring the power of reflected probe beam. The photodetector generates an output signal that is proportional to the reflected power of the probe beam and is therefore indicative of the varying optical reflectivity of the sample surface. The output signal from the photodetector is filtered to isolate the changes that are synchronous with the pump beam modulation frequency. A lock-in detector is typically used to measure both the in-phase (I) and quadrature (Q) components of the detector output. The two channels of the output signal, namely the amplitude A2=I2+Q2 
and phase Θ=arctan(I/Q) are conventionally referred to as the Modulated Optical Reflectance (MOR) or Thermal Wave (TW) signal amplitude and phase, respectively.
Dynamics of the thermal- and carrier plasma-related components of the total MOR signal in a semiconductor is given by the following general equation:
            Δ      ⁢                          ⁢      R        R    =            1      R        ⁢          (                                                  ∂              R                                      ∂              T                                ⁢          Δ          ⁢                                          ⁢                      T            0                          +                                            ∂              R                                      ∂              N                                ⁢          Δ          ⁢                                          ⁢                      N            0                              )      where ΔT0 and ΔN0 are the temperature and the carrier plasma density at the surface of a semiconductor, R is the optical reflectance, dR/dT is the temperature reflectance coefficient and dR/dN is the carrier reflectance coefficient. For silicon, dR/dT is positive in the visible and near-UV part of the spectrum while dR/dN remains negative throughout the entire spectrum region of interest. The difference in sign results in destructive interference between the thermal and plasma waves and decreases the total MOR signal at certain experimental conditions. The magnitude of this effect depends on the nature of a semiconductor sample and on the parameters of the photothermal system, especially on the pump and probe beam wavelengths.
In the early commercial embodiments of the TP device, both the pump and probe laser beams were generated by gas discharge lasers. Specifically, an argon-ion laser emitting a wavelength of 488 nm was used as a pump source. A helium-neon laser operating at 633 nm was used as a source of the probe beam. More recently, solid state laser diodes have been used and are generally more reliable and have a longer lifetime than the gas discharge lasers. In the current commercial embodiment, the pump laser operates at 780 nm while the probe laser operates at 670 nm. The performance of this commercial TP system was significantly improved recently by the introduction of fiber-coupled diode lasers. Examples of the fiber-coupled TP system are given in the U.S. Pat. No. 7,079,249 assigned to the assignee of the current invention and incorporated herein by reference.
In modern semiconductor manufacturing, product wafers pass through multiple processing steps. Different parameters of product wafers are usually monitored after each process step in order to ensure that this particular fabrication step has been performed within specification. Different characteristics of semiconductor wafer are measured. After the two initial processing steps—ion implantation and annealing—several parameters are usually monitored that characterize damage density and electronic properties of the wafer, i.e., ion implantation dose and energy before anneal, active ion concentration, carrier lifetime, carrier mobility, wafer resistivity, etc. after anneal.
In most of these characterizations, uniform or discontinuously inhomogeneous material properties are assumed. This approach significantly simplifies quantitative analysis of the samples at the expense of the accuracy of such measurements. Except for a few situations when this simplifying assumption is valid and provides acceptable results, in most of the cases a continuously inhomogeneous profile of semiconductor material parameters should be considered for the adequate metrology analysis.
As an example, FIG. 1 shows several concentration depth profiles corresponding to different process conditions in manufacturing of semiconductor devices. In this figure, profiles 1 to 4 have been obtained using SIMS (Secondary Ion Mass Spectrometry) from ion-implanted Si wafers that underwent thermal annealing at different temperatures. In an ideal process, all these profiles would have been box-like, e.g., exhibiting an almost instant drop in concentration after the peak. However, such is not the case in real semiconductor manufacturing and profile information should be extracted from the sample for the accurate analysis of its characteristics.
A very limited number of technologies (such as SIMS, RBS—Rutherford Back Scattering, RS—spreading resistance, and others) are used today for parameter depth profiling in semiconductor manufacturing process. SIMS is primarily used to profile carrier concentration while RBS is used for profiling defects in semiconductors induced by ion implantation process. All these techniques are expensive, slow and destructive, i.e., require a special blank monitor wafer for analysis. In addition, production SIMS tools can not currently provide reliable concentration profile information below 100 A. Spreading resistance measurements are faster than SIMS and RBS but not accurate enough in its depth profiling capability. Also, RS technology requires good electrical contacts on both sides of semiconductor wafer which is not possible in most practical situations.
Therefore, there is a need for a fast, reliable non-destructive and non-contact technology capable of providing accurate depth profile information. Non-contact optical methods, such as MOR, are fast, accurate and reliable for characterizing of semiconductors and thin films on semiconducting materials. Thus, it would be desirable to develop an optically-based technology for depth profiling analysis of thermal and electronic properties of semiconductor wafers.
Photothermal and photoacoustic methods have long been used for characterization of different types of materials including semiconductors. In the past, there have been several attempts to use photothermal (a.k.a. opto-thermal) technologies for depth profiling of thermal and electronic properties in semiconductors.
Generally, performing depth profiling requires finding solutions to both forward and inverse problems. The forward problem is usually a theoretical model that takes into account all relevant properties of the sample (including their depth profiles, if needed) and experimental conditions to obtain an accurate description of the physical processes. The solution to the forward problem is a model predicting the signal behavior in practical measurements. The inverse problem is a reverse of the forward problem, e.g., it deals with obtaining sample parameters (including depth profiles) from the results of the experimental measurements. The solution to the inverse problem often involves sophisticated mathematical procedures, fitting algorithms, etc. and, therefore, is usually much more difficult to solve than the forward problem. Finding a solution to the inverse problem, especially for depth profiles in semiconductors, represents the biggest challenge in metrology.
In the past, there were numerous studies of the forward part of the depth profiling problem, especially in the thermal wave domain (e.g., in non-semiconducting materials) while only few studies were performed on the inverse problem in semiconductors.
The first conceptual study of MOR depth profiling capability in semiconductors is described in the article “Thermal and plasma wave depth profiling in silicon”, by J. Opsal and A. Rosencwaig, Appl. Phys. Lett. 47(15), pp. 498-500 (1985), incorporated herein by reference. In this article, the plasma wave dependency on modulation frequency is used to probe semiconductor material at different depths potentially leading to the reconstruction of electronic parameter depth profiles. However, only a two-layer semiconductor sample was discussed in this article to illustrate depth profiling using the plasma wave component of MOR signal. In addition, the solution to the inverse problem was not proposed in this study.
Several studies related to thermal and electronic parameter depth profiling including both forward and inverse problems using Photothermal Radiometry (PTR) technique have been performed by A. Mandelis and his group at the University of Toronto and described in two publications. Thermal diffusivity depth profiling concept is presented in the article “Generalized methodology for thermal diffusivity depth profile reconstruction in semi-infinite and finitely thick inhomogeneous solids”, by A. Mandelis, F. Funak, and M. Munidasa, J. Appl. Phys. 80(10), pp. 5570-5579 (1996), and depth profiling of electronic parameters in semiconductors using PTR is described in the article “Hamiltonian plasma-harmonic oscillator theory: Generalized depth profilometry of electronically continuously inhomogeneous semiconductors and the inverse problem”, by A. Salnik and A. Mandelis, J. Appl. Phys. 80(9), pp. 5278-5288 (1996). Both papers are incorporated herein by reference.
In these papers, the Hamiltonian-Jacobi formalism of the propagation of the thermal and plasma waves in continuously inhomogeneous semiconductors is presented and a reconstruction of thermal diffusivity (thermal properties) and carrier lifetime (electronic properties) depth profiles is demonstrated. The solutions to the inverse problem in both cases (thermal and plasma parameters) were based on modulation frequency dependencies of the PTR signal. Thermal diffusivity depth profiles were successfully calculated from the experimental data while carrier lifetime depth profiles were only partially determined. This was due to the very specific nature of the plasma waves: these waves are frequency-independent at low modulation frequencies when ωτ<<1 and they are lifetime-independent at high modulation frequencies when ωτ>>1, while thermal waves are both frequency and thermal diffusivity-dependent at all modulation frequencies. This fundamental limitation of plasma waves makes it impossible to use frequency domain measurements for electronic parameter depth profiling in semiconductors.
Another attempt to solve the inverse problem in depth profiling of ultra-shallow junctions (USJ) formed in semiconductor materials is presented in the article “Carrier illumination for characterization of ultra-shallow doping profiles”, by T. Clarysse, et al., Book of Abstracts, 7th Int. Workshop on: Fabrication, Characterization, and Modeling of USJ Doping Profiles in Semiconductors (USJ-2003), Santa Cruz, Calif., Apr. 27-May 1, 2003, pp. 321-327, incorporated herein by reference. In this paper, an MOR-like experimental system was used to obtain signal dependencies on pump beam power. A solution to the inverse problem was not discussed in this publication. However, FIG. 2 herein schematically illustrated two box-like approximations to the real concentration profiles of the type that could have been used by Clarysse to create a simplified theoretical model for obtaining concentration depth profiles. As shown in FIG. 2, these box-like approximations (discontinuously inhomogeneous approximations), being relatively easy to invert, provide only a zero-order approximation to the real profile shape (continuously inhomogeneous). Therefore, box-like profiles can not be used for the accurate reconstruction of depth profiles.
To summarize, the current state of the art in depth profiling of continuously inhomogeneous electronic properties in surface modified semiconductors (i.e., ion-implanted Si and USJ) concentrates on solving only the forward part of the problem. A very few attempts to solve the inverse part of this depth profiling problem have failed to provide an accurate, reliable and sensitive enough technique that is required for applications in modern semiconductor manufacturing.